PRINCETON – On January 1, Derek Parfit, one of the greatest philosophers of my generation, died. Just a year earlier, in a poll on a leading philosophy website, Parfit had been voted the most important living Anglophone philosopher.

Of all the philosophers I have known since I began to study the subject more than 50 years ago, Parfit was the closest to a genius. Getting into a philosophical argument with him was like playing chess with a grandmaster: he had already thought of every response I could make to his arguments, considered several possible replies, and knew the objections to each reply as well as the best counters to those objections.

Parfit was not a household name. Few people outside the world of academic philosophy have read anything he wrote. Nor did he appear on television, although late in life, he spoke about effective altruism, and two of those talks can be seen online.

He also published very little before his first book, Reasons and Persons, came out in 1984, when he was 42 years old. His readers then had to wait another 27 years for his second book, On What Matters, unless they were able to read one of the drafts that Parfit circulated in order to receive suggestions for improvement.

To say that Parfit wrote only two books, however, is misleading. Reasons and Persons brings together novel ideas on three separate topics. First, he discusses theories of rational action. Is it rational always to act in our own interests, or to act in accordance with our present desires, or to bring about the best consequences for everyone, timelessly?

The second topic is personal identity. Whereas we commonly take the distinction between our self and others as an all-or-nothing matter, because we assume that we are the same person throughout our life, Parfit argued that our identity changes over time as the psychological connections between our earlier and later selves alter. Parfit found this view liberating: "Other people are closer," he wrote, "I am less concerned about the rest of my own life and more concerned about the lives of others."

In the final part of the book, Parfit asked: What is the optimum population for a country, or a planet? Should we aim for the greatest possible total quantity of happiness, or the highest average level of happiness?

Assuming that the average level of happiness is positive, these choices will diverge if increasing the planet's population will reduce the average, but not by enough to offset the fact that now more happy people exist. In thinking about this question, we can put aside the environmental constraints that provide reasons for not increasing the population, because Parfit is trying to get at an underlying question of value. He shows that both the "total" and "average" answers have paradoxical or counter-intuitive implications. But then, so does every other answer that has been proposed since Parfit revived the problem and other philosophers began to offer their own solutions.

If Reasons and Persons could easily have been three separate books, On What Matters really is: the first two volumes were published in 2011, while a third, in press when Parfit died, has just appeared. In this monumental work, totaling about 1,900 pages, Parfit challenges the idea – almost universally assumed by economists, and by many philosophers from David Hume onward – that the role of reason is to tell us how to get what we want, but not to tell us what to want.

On the contrary, Parfit argued, desires can be irrational. It is, for example, irrational to wish to avoid agonizing pain every day of the week except any future Tuesday.

In order to show that there can be objective truths in ethics, Parfit boldly sought to reconcile three major normative theories: Kantianism, contractualism, and consequentialism. Adherents of each of these theories are, Parfit suggested, "climbing the same mountain on different sides," taking their own routes to a common element of truth in each theory.

In On What Matters, Volume Three, Parfit again tried to reconcile three major theories, this time theories about the nature of ethics, and the basis on which one might call an ethical judgment "true."

Parfit was not only a remarkable philosopher; he was also extraordinarily generous with the resource that was most precious to him: his time. So concerned was he about not wasting time that he read philosophy while brushing his teeth, and his wardrobe was full of identical shirts and suits so that he would not have to think about what to wear. Yet when students or colleagues sent him work, he would read it and, whether he agreed with it or not, write detailed comments, sometimes longer than the work itself. I benefited from that, as did countless others.

I will let Parfit have the last word. At a time when many people are despairing about current political trends, the penultimate paragraph of On What Matters, Volume Three encourages us to take a longer and more optimistic perspective:

"Life can be wonderful as well as terrible, and we shall increasingly have the power to make life good. Since human history may be only just beginning, we can expect that future humans, or supra-humans, may achieve some great goods that we cannot now even imagine. In Nietzsche's words, there has never been such a new dawn and clear horizon, and such an open sea."

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Peter Singer is Professor of Bioethics at Princeton University and Laureate Professor at the University of Melbourne. He is the editor of Does Anything Really Matter? Essays on Parfit on Objectivity, which has just been published as a companion volume to Parfit's On What Matters, Volume Three.